I don't think people really worry about defining closing time. They close when everyone is gone or they're done for the day. I know that this doesn't help much, but it kind of should help. Most of Greece is like this, and other European countries, as well.
I swear Greece is one of the only places where visiting monasteries is like a must do! Toplou monastery is so stunning and I highly recommend it for anyone who wants to see some less touristy sites in Greece!